The Gallup organization conducted a survey with a random sample of 1,019 adult A

Question

The Gallup organization conducted a survey with a random sample of 1,019 adult Americans on December 10–12, 2010. They found that 80% of the respondents agreed with the statement that the United States has a unique character that makes it the greatest country in the world.

1A. Is it reasonable to believe that the sample of 1, 019 adult Americans is representative of the larger population? Explain why or why not.

B. Identify (in words) the parameter that the Gallup organization was interested in estimating.

C. Is it reasonable to conclude that exactly 80% of all Adult Americans agree with the statement about American exceptionalism? Explain why or why not.

Explanation / Answer

(a)

No it is not reasonable to assume that the sample is representative of the whole population, because there may be many types of bias which could be present. For instance, if all those people were sampled from a particular state which has patriotic people, then definitely most of them would feel that their country is great. This sample can not be considered representative and additional data needs to be analyzed.

(b)

The parameter in which the organization is interested is the proportion of Americans who feel that their country is greatest because of a unique character.

(c)

No, firstly because the sample is not representative and this result may be biased.

Secondly, even if we assume that the sample is unbiased, then we need to confirm the significance of this result by a hypothesis testing, because it could also be the case that such a sample was collected by pure chance, while the population proportion is quite different as a whole.

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